Data Visualization with ggplot2

class: center, middle, inverse, title-slide

.title[
# Data Visualization with ggplot2
]
.author[
### John Tipton
]

---

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# Readings

* R for data science 
    * Introduction
    * Chapters 1 (Data visualization with `ggplot2`) and 5 (Exploratory data analysis)

---

# `data.frame` The first class object

* A `data.frame` is a rectangular collection of variables (columns) and observations (rows).

* Built in datasets can be explored with `data()`

```r
data()
```

---

# Example: Palmer Penguins

```r
library(tidyverse)
library(palmerpenguins)
```

.small[

```r
penguins
```

```
## # A tibble: 344 × 8
##    species island    bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex     year
##    <fct>   <fct>              <dbl>         <dbl>             <int>       <int> <fct>  <int>
##  1 Adelie  Torgersen           39.1          18.7               181        3750 male    2007
##  2 Adelie  Torgersen           39.5          17.4               186        3800 female  2007
##  3 Adelie  Torgersen           40.3          18                 195        3250 female  2007
##  4 Adelie  Torgersen           NA            NA                  NA          NA <NA>    2007
##  5 Adelie  Torgersen           36.7          19.3               193        3450 female  2007
##  6 Adelie  Torgersen           39.3          20.6               190        3650 male    2007
##  7 Adelie  Torgersen           38.9          17.8               181        3625 female  2007
##  8 Adelie  Torgersen           39.2          19.6               195        4675 male    2007
##  9 Adelie  Torgersen           34.1          18.1               193        3475 <NA>    2007
## 10 Adelie  Torgersen           42            20.2               190        4250 <NA>    2007
## # … with 334 more rows
```
]

---

# First ggplot

* start by exploring the data. Use the `str()` or `glimpse()` functions to explore the data

.small[

```r
str(penguins)
```

```
## tibble [344 × 8] (S3: tbl_df/tbl/data.frame)
##  $ species          : Factor w/ 3 levels "Adelie","Chinstrap",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ island           : Factor w/ 3 levels "Biscoe","Dream",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ bill_length_mm   : num [1:344] 39.1 39.5 40.3 NA 36.7 39.3 38.9 39.2 34.1 42 ...
##  $ bill_depth_mm    : num [1:344] 18.7 17.4 18 NA 19.3 20.6 17.8 19.6 18.1 20.2 ...
##  $ flipper_length_mm: int [1:344] 181 186 195 NA 193 190 181 195 193 190 ...
##  $ body_mass_g      : int [1:344] 3750 3800 3250 NA 3450 3650 3625 4675 3475 4250 ...
##  $ sex              : Factor w/ 2 levels "female","male": 2 1 1 NA 1 2 1 2 NA NA ...
##  $ year             : int [1:344] 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 ...
```
]

.small[

```r
glimpse(penguins)
```

```
## Rows: 344
## Columns: 8
## $ species           <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adel…
## $ island            <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgersen, Torgersen, Torgersen, Torgersen, Torg…
## $ bill_length_mm    <dbl> 39.10000000000000142109, 39.50000000000000000000, 40.29999999999999715783, NA, 36.7000000000…
## $ bill_depth_mm     <dbl> 18.69999999999999928946, 17.39999999999999857891, 18.00000000000000000000, NA, 19.3000000000…
## $ flipper_length_mm <int> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186, 180, 182, 191, 198, 185, 195, 197, 184…
## $ body_mass_g       <int> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, 4250, 3300, 3700, 3200, 3800, 4400, 3700…
## $ sex               <fct> male, female, female, NA, female, male, female, male, NA, NA, NA, NA, female, male, male, fe…
## $ year              <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 20…
```
]

---

# flipper length and body mass

* Describe what we see

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm))
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

# Plotting aesthetics

* ggplot is a lot of code for a simple plot!

```r
plot(flipper_length_mm ~ body_mass_g, data = penguins)
```

* Wasn't that easier?

---

# Aesthetics

- What if I want to color my plot by sex?

- What if I want to make my circles to have size relative to bill depth?

- What if...

* Use aesthetics.

* Aesthetics map a characteristic given a variable.
    
    * Great for quick visually communication.

---

# Using aesthetics

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm,
                             color = sex))
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

# Using aesthetics

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm,
                             color = sex, size = bill_length_mm))
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

# Available aesthetics

* size

* color

* fill

* shape

* transparency (`alpha`)

---

# Facets

* What if I want to show multiple plots where each plot is determined by a variable?

* Facets.

* `facet_wrap()` for a single variable.
    
    * `facet_grid()` for a grid of two variables.
    
---

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm)) +
    facet_wrap(~ sex)
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm)) +
    facet_grid(island ~ sex)
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

# Geometries

* What kind of plot do you want?

* histograms --`geom_histogram()`
    * scatterplot -- `geom_point()`
    * boxplots -- `geom_box()`
    * dotplot -- `geom_dotplot()`
    * line plots -- `geom_line()`
    
* Each `geom` has specific aesthetic requirements

* Use the help for specifics
    * `?geom_scatter`

* Many, many others -- virtually any kind of plot you want.
    * [ggplot cheatsheet](https://rstudio.com/wp-content/uploads/2015/03/ggplot2-cheatsheet.pdf)

* Many custom packages for specific plot types

---

```r
ggplot(data = penguins) +
    geom_histogram(mapping = aes(x = body_mass_g))
```

```
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
```

```
## Warning: Removed 2 rows containing non-finite values (stat_bin).
```

---

```r
## what happens if you use color = sex?
ggplot(data = penguins) +
    geom_histogram(mapping = aes(x = body_mass_g, fill = sex)) 
```

```
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
```

```
## Warning: Removed 2 rows containing non-finite values (stat_bin).
```

---

```r
## smooth over the density
ggplot(data = penguins) +
    geom_violin(mapping = aes(y = body_mass_g, x = sex)) 
```

```
## Warning: Removed 2 rows containing non-finite values (stat_ydensity).
```

---

```r
## what happens if you use color = sex?
ggplot(data = penguins) +
    geom_boxplot(mapping = aes(x = body_mass_g, fill = sex)) 
```

```
## Warning: Removed 2 rows containing non-finite values (stat_boxplot).
```

---

* You can even use multiple aesthetics

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm)) +
    geom_smooth(mapping = aes(x = body_mass_g, y = flipper_length_mm))
```

```
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
```

```
## Warning: Removed 2 rows containing non-finite values (stat_smooth).
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

* geoms can have different aesthetics `aes()`.

```r
ggplot(data = penguins) +
    geom_point(mapping = aes(x = body_mass_g, y = flipper_length_mm,
                             color = sex)) +
    geom_smooth(mapping = aes(x = body_mass_g, y = flipper_length_mm, 
                              fill = sex, color = sex))
```

```
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
```

```
## Warning: Removed 2 rows containing non-finite values (stat_smooth).
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

* Common aesthetics `aes()` can be added to the ggplot function.

```r
ggplot(data = penguins,
       mapping = aes(x = body_mass_g, y = flipper_length_mm, color = sex)) +
    geom_point() +
    geom_smooth(mapping = aes(fill = sex))
```

```
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
```

```
## Warning: Removed 2 rows containing non-finite values (stat_smooth).
```

```
## Warning: Removed 2 rows containing missing values (geom_point).
```

---

# Statistical transformations

* `ggplot` can perform statistical transformations and fit basic models

* start with `starwars` data

```r
data("starwars")
glimpse(starwars)
```

```
## Rows: 87
## Columns: 14
## $ name       <chr> "Luke Skywalker", "C-3PO", "R2-D2", "Darth Vader", "Leia Organa", "Owen Lars", "Beru Whitesun lars"…
## $ height     <int> 172, 167, 96, 202, 150, 178, 165, 97, 183, 182, 188, 180, 228, 180, 173, 175, 170, 180, 66, 170, 18…
## $ mass       <dbl> 77.00000000000000000000, 75.00000000000000000000, 32.00000000000000000000, 136.00000000000000000000…
## $ hair_color <chr> "blond", NA, NA, "none", "brown", "brown, grey", "brown", NA, "black", "auburn, white", "blond", "a…
## $ skin_color <chr> "fair", "gold", "white, blue", "white", "light", "light", "light", "white, red", "light", "fair", "…
## $ eye_color  <chr> "blue", "yellow", "red", "yellow", "brown", "blue", "blue", "red", "brown", "blue-gray", "blue", "b…
## $ birth_year <dbl> 19.00000000000000000000, 112.00000000000000000000, 33.00000000000000000000, 41.89999999999999857891…
## $ sex        <chr> "male", "none", "none", "male", "female", "male", "female", "none", "male", "male", "male", "male",…
## $ gender     <chr> "masculine", "masculine", "masculine", "masculine", "feminine", "masculine", "feminine", "masculine…
## $ homeworld  <chr> "Tatooine", "Tatooine", "Naboo", "Tatooine", "Alderaan", "Tatooine", "Tatooine", "Tatooine", "Tatoo…
## $ species    <chr> "Human", "Droid", "Droid", "Human", "Human", "Human", "Human", "Droid", "Human", "Human", "Human", …
## $ films      <list> <"The Empire Strikes Back", "Revenge of the Sith", "Return of the Jedi", "A New Hope", "The Force …
## $ vehicles   <list> <"Snowspeeder", "Imperial Speeder Bike">, <>, <>, <>, "Imperial Speeder Bike", <>, <>, <>, <>, "Tr…
## $ starships  <list> <"X-wing", "Imperial shuttle">, <>, <>, "TIE Advanced x1", <>, <>, <>, <>, "X-wing", <"Jedi starfi…
```

---

# Bar plot

```r
ggplot(data = starwars, mapping = aes(x = sex)) +
  geom_bar()
```

---

# Bar plot using statistics

* count the number in each category of sex

```r
ggplot(data = starwars, mapping = aes(x = sex)) +
  stat_count()
```

---

# Bar plot using statistics

* count the number in each category of sex

```r
ggplot(data = starwars, mapping = aes(x = sex)) +
  geom_bar(stat = "count")
```

---

# Bar plot using statistics

* The relative number in each category of sex

```r
ggplot(data = starwars, mapping = aes(x = sex, y = stat(prop), group = 1)) +
  geom_bar()
```

---

# `stat_summary`

* plot the extent of the

```r
ggplot(data = starwars, aes(x = sex, y = height)) +
  stat_summary(
    fun.min = min,
    fun.max = max,
    fun     = mean
  )
```

```
## Warning: Removed 6 rows containing non-finite values (stat_summary).
```

---

# `stat_summary`

* Plot the quantiles

```r
ggplot(data = starwars, aes(x = sex, y = height)) +
  stat_summary(
    fun.min = function(z) quantile(z, prob = 0.1),
    fun.max = function(z) quantile(z, prob = 0.9),
    fun     = median
  )
```

```
## Warning: Removed 6 rows containing non-finite values (stat_summary).
```

---

# Plotting big data

* Use binning

```r
ggplot(data = penguins, aes(x = body_mass_g, y = flipper_length_mm)) +
    geom_hex()
```

```
## Warning: Removed 2 rows containing non-finite values (stat_binhex).
```

---

# Positions

* can use fill and color to highlight subsets of data

* positions of "dodge" and "jitter" can improve visualization.

.pull-left[

```r
ggplot(penguins, aes(x = species)) +
  geom_bar()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-left-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-right-1.png" width="80%" style="display: block; margin: auto;" />
]

---

* position = "fill"

.pull-left[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-left2-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar(position = "fill")
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-right2-1.png" width="80%" style="display: block; margin: auto;" />
]

---

* position = "identity"

* notice these are overlapping

.pull-left[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-left3-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar(position = "identity", alpha = 0.5)
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-right3-1.png" width="80%" style="display: block; margin: auto;" />
]

---

* position = "dodge"

.pull-left[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-left4-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(penguins, aes(x = species, fill = island)) +
  geom_bar(position = "dodge")
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-right4-1.png" width="80%" style="display: block; margin: auto;" />
]

---

* position = "jitter"

* use the built-in `mpg` dataset

```r
glimpse(mpg)
```

```
## Rows: 234
## Columns: 11
## $ manufacturer <chr> "audi", "audi", "audi", "audi", "audi", "audi", "audi", "audi", "audi", "audi", "audi", "audi", "…
## $ model        <chr> "a4", "a4", "a4", "a4", "a4", "a4", "a4", "a4 quattro", "a4 quattro", "a4 quattro", "a4 quattro",…
## $ displ        <dbl> 1.800000000000000044409, 1.800000000000000044409, 2.000000000000000000000, 2.00000000000000000000…
## $ year         <int> 1999, 1999, 2008, 2008, 1999, 1999, 2008, 1999, 1999, 2008, 2008, 1999, 1999, 2008, 2008, 1999, 2…
## $ cyl          <int> 4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4…
## $ trans        <chr> "auto(l5)", "manual(m5)", "manual(m6)", "auto(av)", "auto(l5)", "manual(m5)", "auto(av)", "manual…
## $ drv          <chr> "f", "f", "f", "f", "f", "f", "f", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "r", "r…
## $ cty          <int> 18, 21, 20, 21, 16, 18, 18, 18, 16, 20, 19, 15, 17, 17, 15, 15, 17, 16, 14, 11, 14, 13, 12, 16, 1…
## $ hwy          <int> 29, 29, 31, 30, 26, 26, 27, 26, 25, 28, 27, 25, 25, 25, 25, 24, 25, 23, 20, 15, 20, 17, 17, 26, 2…
## $ fl           <chr> "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "r", "e…
## $ class        <chr> "compact", "compact", "compact", "compact", "compact", "compact", "compact", "compact", "compact"…
```

---

# Positions

* position = "jitter"

* Useful when observations overlap

.pull-left[

```r
ggplot(mpg, aes(x = displ, y = hwy)) +
  geom_point()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-left5-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(mpg, aes(x = displ, y = hwy)) +
  geom_point(position = "jitter")
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/bar-right5-1.png" width="80%" style="display: block; margin: auto;" />
]

---

# Positions

* position = "jitter"

.pull-left[

```r
ggplot(mpg, aes(x = trans, y = hwy)) +
  geom_boxplot() +
  geom_point()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/box-jitter1-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

```r
ggplot(mpg, aes(x = trans, y = hwy)) +
  geom_boxplot() +
  geom_point(position = "jitter")
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/box-jitter2-1.png" width="80%" style="display: block; margin: auto;" />
]

---

# Exploratory Data Analysis

* EDA is an artform

* Explore and learn from the data

* Guides model development

* Identifies transformations of the data that might be helpful

* Helps in formulating questions about the data

* Express creativity!

---

# Tidy data

* Each row is an observation

* An observation is a set of measurements about an element
    
    * The element is the object on which measurement is made

* Each column is a variable

* A variable is a characteristic of the element that can take on an value
    
* Tidy data is tabular where each row is an observation and each column is a variable

```r
str(diamonds)
```

```
## tibble [53,940 × 10] (S3: tbl_df/tbl/data.frame)
##  $ carat  : num [1:53940] 0.23 0.21 0.23 0.29 0.31 0.24 0.24 0.26 0.22 0.23 ...
##  $ cut    : Ord.factor w/ 5 levels "Fair"<"Good"<..: 5 4 2 4 2 3 3 3 1 3 ...
##  $ color  : Ord.factor w/ 7 levels "D"<"E"<"F"<"G"<..: 2 2 2 6 7 7 6 5 2 5 ...
##  $ clarity: Ord.factor w/ 8 levels "I1"<"SI2"<"SI1"<..: 2 3 5 4 2 6 7 3 4 5 ...
##  $ depth  : num [1:53940] 61.5 59.8 56.9 62.4 63.3 62.8 62.3 61.9 65.1 59.4 ...
##  $ table  : num [1:53940] 55 61 65 58 58 57 57 55 61 61 ...
##  $ price  : int [1:53940] 326 326 327 334 335 336 336 337 337 338 ...
##  $ x      : num [1:53940] 3.95 3.89 4.05 4.2 4.34 3.94 3.95 4.07 3.87 4 ...
##  $ y      : num [1:53940] 3.98 3.84 4.07 4.23 4.35 3.96 3.98 4.11 3.78 4.05 ...
##  $ z      : num [1:53940] 2.43 2.31 2.31 2.63 2.75 2.48 2.47 2.53 2.49 2.39 ...
```

# EDA

* Measures of central tendency

* mean, median, mode

* Measures of variability

* variance/standard deviation, range, IQR/quantiles
    
* Missing values?

* What do you do with missing values?
    
    * What about outliers/unusual observations?

* Covariance

* Outliers/unusal values

---

# Distributions

* Visualize marginal (one variable) distributions

* histograms `geom_histogram()`
    
    * density plots `geom_dens()`
    
    * boxplots `geom_boxplot()`
    
    * violin plots `geom_violin()`

---

# Distributions
    
.pull-left[

```r
ggplot(diamonds, aes(x = price)) +
  geom_histogram()
```

```r
ggplot(diamonds, aes(x = price)) +
  geom_density()
```

]

.pull-right[

```r
ggplot(diamonds, aes(x = cut, y = price)) +
  geom_boxplot()
```

```r
ggplot(diamonds, aes(x = cut, y = price)) +
  geom_violin()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/unnamed-chunk-13-1.png" width="80%" style="display: block; margin: auto;" />
]

---

# Missing values

* As a rule, don't just ignore missing values blindly

* I conduct a survey about income and leisure time. Why shouldn't I ignore those people that don't respond?
    
* Many functions have a `na.rm` option

```r
mean(penguins$bill_length_mm)
```

```
## [1] NA
```

```r
mean(penguins$bill_length_mm, na.rm = TRUE)
```

```
## [1] 43.92192982456140271097
```
   
---

# Missing values

.pull-left[

* Notice the warning

```r
ggplot(penguins, aes(y = bill_length_mm)) +
  geom_boxplot()
```

```
## Warning: Removed 2 rows containing non-finite values (stat_boxplot).
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/unnamed-chunk-15-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

* No warning with `na.rm = TRUE`

```r
ggplot(penguins, aes(y = bill_length_mm)) +
  geom_boxplot(na.rm = TRUE)
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/unnamed-chunk-16-1.png" width="80%" style="display: block; margin: auto;" />
]

---

# Missing values

* What if missing values are important?

* `airquality` dataset is missing the Ozone variable in June.

.pull-left[

* Ozone measurements vs. Month

```r
airquality %>%
  ggplot(aes(x = factor(Month), y = Ozone)) +
  geom_boxplot()
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/unnamed-chunk-17-1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[

* Missing values vs. Month

```r
airquality %>%
  mutate(missing_ozone = is.na(Ozone)) %>%
  ggplot(aes(fill = missing_ozone, x = Month)) +
  geom_density(alpha = 0.5)
```

<img src="data:image/png;base64,#unit_4_R_10_intro_plotting_files/figure-html/unnamed-chunk-18-1.png" width="80%" style="display: block; margin: auto;" />
]

---

# Covariation

* Statistical modeling is about finding patterns and covariation in data

* Is there a relationship between bill depth and bill length?

```r
ggplot(penguins, aes(x = bill_length_mm, y = bill_depth_mm)) +
  geom_point() +
  stat_smooth(method = "lm")
```

---

# Covariation

* Statistical modeling is about finding patterns and covariation in data

* Is there a relationship between bill depth and bill length?

```r
ggplot(penguins, aes(x = bill_length_mm, y = bill_depth_mm, color = sex)) +
  geom_point() +
  stat_smooth(method = "lm")
```

---

# Covariation

* Statistical modeling is about finding patterns and covariation in data

* Is there a relationship between bill depth and bill length?

```r
ggplot(penguins, aes(x = bill_length_mm, y = bill_depth_mm, color = species)) +
  geom_point() +
  stat_smooth(method = "lm")
```

---

# Covariation

* Statistical modeling is about finding patterns and covariation in data

* Is there a relationship between bill depth and bill length?

```r
ggplot(penguins, aes(x = bill_length_mm, y = bill_depth_mm, color = species)) +
  geom_point() +
  facet_wrap(~ sex) +
  stat_smooth(method = "lm")
```

---

# Pairs plots

```r
penguins %>%
  select(species, body_mass_g, ends_with("_mm")) %>%
  GGally::ggpairs(aes(color = species)) +
  scale_colour_manual(values = c("darkorange", "purple", "cyan4")) +
  scale_fill_manual(values = c("darkorange", "purple", "cyan4"))
```

---

# Namespaces

* What's the deal with the `GGally::ggpairs()` function on the last slide?

* Often in programming there are different packages that have functions with the same name 
    * The **namespace** resolves this issue
    
    * Use the `ggpairs` function from the `GGally` package